The exp function works for complex inputs: >> z = 1 + 2i z = 1.0000 + 2.0000i >> exp(z) ans = -1.1312 + 2.4717i If you want something else you will need to be more specific with your question.

One approach is to use the rewrite and simplify functions: syms t y = exp(t*(4 - 2i))/2 + exp(t*(4 + 2i))/2 Y = simplify(rewrite(y, 'sin'), 'Steps', 50) producing: y = exp(t*(4 - 2i))/2 + exp(t*(4 + 2i))/2 Y = cos(2*t)*exp(4*t) See the documentation for the fucntions for details and examples.

Hi Jogger, have a look at Euler's formula (https://en.wikipedia.org/wiki/Euler's_formula). x = 2 + 1j * 5; r = sqrt(real(x)^2 + imag(x)^2); phi = atan2(imag(x),real(x)); fprintf(1,'z = r * exp(j*phi)\nr = %.2f\nphi = %.2f',r,phi) Kind regards, Robert

I am not certain what you are doing or what ‘w1’ and ‘w2’ are, so using my best guess — format longE F = 40E+3; N = (0:20).'; omega1 = 2*pi*F; % Guessing: 'W1' omega2 = 4*pi*F; % Guessing: 'w2' X = exp(1j*omega1*N) + exp(1j*omega2*N) .

exp(1i*pi/6./t) or exp(1i*pi/6.*t) depending on whether the t is intended to be in the numerator or denominator

First of all, you try to make a plot of complex numbers z_n. This does not make any sense. You can plot the real part (real(z_n), the imaginary part (imag(z_n) or the absolute values (abs(z_n).

However, your exceptions in the second diagram are wrong too. Your function exp(j2πmf) is a rotating vector with absolute amplitude 1.

This results in:

1. real(exp(j2πmf) = cos(2πmf)
2. imag (exp(j2πmf) = sin(2πmf); By the way, imag does not include j, it is the value which has j as a factor.
3. abs(exp(j2πmf) = 1

This approximates it: t = linspace(0, 2.5, 250); f = exp(2*pi*4/2.5*1i*t); figure(1) plot3(t, real(f), imag(f), 'LineWidth',2) hold on plot3(t, real(f), zeros(size(t))-1.5) plot3(t, zeros(size(t))-2, imag(f)) hold off grid on axis([-1 3 -2 2 -1.5 1.5]) view([-125 30]) xlabel('Time', 'Rotation',-30) ylabel('Real Axis', 'Rotation',10) zlabel('Imag Axis') <> If you want to add the labels, see the documetation for the function.